Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
The rank of a Lie group is the dimension of any one of its Cartan subgroups, hence equivalently the dimension of any one of the Cartan subalgebras of its Lie algebra.
For connected compact Lie groups, a Cartan subgroup is a maximal torus, and hence in this case the rank of the Lie group is the dimension of any one of its maximal tori.
Last revised on December 8, 2024 at 20:19:18. See the history of this page for a list of all contributions to it.